where \(\rho \)  is the density in the layer, \(\beta _0\)  is the thermal expansion coefficient and we used \(\beta _0\,=\,10^{-3}\)  as a safe upper limit for any of the possible constituents, \(\Delta \) T is the temperature difference across distance \(dr\) , which is the thickness of the layer, \(k_0\)  is the permeability, and we used two values: \(10^{-12}\,m^2\)  following [1]} and \(10^{-7}\,m^2\)  following [2]}. The results were the same because the Ra did not reach the critical value required for the start of convection with any of the permeability values. \(g\)  is the local gravitational acceleration, \(\alpha = k/(\rho \cdot c_p)\)  is the thermal diffusivity (\(k\)  is thermal conductivity and \(c_p\)  is specific heat capacity) and \(\eta \)  is the dynamic viscosity of the fluid:
\(\eta (T) = \eta _0 \, exp(25\times (T_{melt}/T-1))\) 
